Student Ability Evaluation using the Stress-Strength Model When Ability is the Random Variable


Takenori Sakumura, Hideo Hirose

The 2010 International Congress on Computer Applications and Computational Science (CACS 2010) Paramount Hotel, 4-6 December 2010, Singapore

Although the item response theory, the IRT, has been widely used to test systems such as the Test of English as a Foreign Language (TOEFL), it is not yet known to teachers in universities and colleges. The superiority of the IRT over the classical test method is also valid in many subjects in universities and high schools. In mathematics tests, the number of problems to be tested in a short time period is strictly limited, particularly in universities, which strongly requires an accurate and efficient method to evaluate the abilities of students. In this paper, we propose to use the stress-strength model (the SS), or its Bayes extension (the SSB), to estimate the studentfs abilities when the abilities are assumed to be the random variables. In the SS and SSB models, parameters to each problem are also assumed the random variables. In estimation, we use the marginal maximum likelihood estimation method and the EM algorithm; to the SSB, the Bayes estimation method is used in addition. Comparing the results by the SS and the SSB models with those by the conventional IRT model, the SS and the SSB show rather stable estimates.

Key Words
evaluation; item response theory; stress- strength model; marginal maximum likelihood estimation; Bayes estimation; EM algorithm.



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